Sal solves the following word problem: You have 50 ounces of a 25% saline solution .How many ounces of 10% saline solution must you add to make a solution that is 15% saline ?

Answer:

x=18

Step-by-step explanation:

We need to find the areas of the rectangles

1st rectangle

A= l*w

A = (2x+4)*9

   = 18x+36

2nd rectangle

A = l*w

   = 15*(3x-30)

    = 45x-450

Since the area of the rectangles are equal, we set these two equations equal

18x+36 = 45x-450

Subtract 18x from each side

18x-18x+36 = 45x-18x-450

36 = 27x-450

Add 450 to each side

36+450 =27x

486 = 27x

Divide by 27 on each side

486/27 = 27x/27

18=x

[tex]i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}[/tex]

Answer:

B = 2

Step-by-step explanation:

using the rule of exponents

• [tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]

consider [tex]83^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{83^{2} }[/tex]

⇒ B = 2

Answer:

21100%

Step-by-step explanation:

Move the decimal point two places to the right.

Answer: I believe that A is the correct answer.

Answer:

It's A

Step-by-step explanation:

I  just did this question

Answer:

[tex]\dfrac{12}{x-7},[/tex]

[tex]x\neq 7,\ x\neq -3.[/tex]

Step-by-step explanation:

Consider the expression

[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]

1. The numerator can be factored as

[tex]12x+36=12(x+3).[/tex]

2. The denominator [tex]x^2-4x-21[/tex] has the discriminant

[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]

Then

[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]

Then

[tex]x^2-4x-21=(x-7)(x+3).[/tex]

Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]

3. Simplify the fraction:

[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]

I honestly don't know or I would have replied. Sorry :(

Answer:  y = -2

========================================

Explanation:

Find the slope of line m using the slope formula

slopeM = (y2-y1)/(x2-x1)

slopeM = (2-8)/(-1-6)

slopeM = -6/(-7)

slopeM = 6/7

The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes

We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.

slopeN = (y2-y1)/(x2-x1)

slopeN = (y-5)/(5-(-1))

slopeN = (y-5)/(6)

-7/6 = (y-5)/6

-7*6 = 6(y-5)

-42 = 6y-30

6y-30 = -42

6y = -42+30

6y = -12

y = -2

So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...

slopeN = (y2-y1)/(x2-x1)

slopeN = (-2-5)/(5-(-1))

slopeN = (-2-5)/(5+1)

slopeN = -7/6

which is the proper slope value we want.

Answer:

$385.49

Step-by-step explanation:

285x1.35261=385.49385

round to the nearest cent and you get $385.49

To exchange 285 Euros for US dollars at an exchange rate of 1.35261, you would receive 385.80785 US dollars.

Current exchange rate = 1.35261 US dollars

To calculate how many dollars would be exchanged for 285 Euros at an exchange rate of 1.35261 US dollars per Euro:

Set up a simple multiplication problem: 285 Euros multiplied by 1.35261 US dollars per Euro.

Multiply the two numbers to get the total amount in US dollars.

So, 285 Euros x 1.35261 = 385.80785 US dollars would be exchanged for 285 Euros.

Answer:

Measures of all angles is either 77.5° or 102.5°

Step-by-step explanation:

See the attached figure.

As shown:

line a parallel to line b with transversal m

So, all the angles are either congruent or supplementary.

Let the supplementary angles x and y and y > x

x + y = 180° ⇒ (1)

one angle is 25° bigger than another

y - x = 25° ⇒ (2)

solving (1) and (2)

∴ x = 77.5°  and y = 102.5°

The side measure of the largest-sized square tile will be 4 in.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Given that, The top of a stepping stone  is 24 inches by 20 inches.

GCF of 24 and 20 = 4

Hence, The side measure of the largest-sized square tile will be 4 in.

For more references on GCF, click;

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A. Negative Association

C. Strong Association

E. Linear

Answer:

1. Negative Correlation

3. Strong Correlation

5. Linear

Step-by-step explanation:

We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.

Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.

We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.

We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.

If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.

The mother can make 3 green curtains and 5 white curtains, using the greatest common divisor of 75 and 125 yards which is 25. Each curtain would thus be 25 yards.

This question can be solved using the concept of Greatest Common Divisor (GCD), which finds the largest possible length that can divide two given lengths without leaving any remainder. In this case, the lengths are 75 yards and 125 yards, which are the quantities of green and white fabric respectively. The GCD of 75 and 125 is 25.

Therefore, the largest number of curtains that can be made is based on this length, which means the mother can make 75/25=3 green curtains and 125/25=5 white curtains. Each curtain would be 25 yards.

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Substitution method

y = x + 3   (*)

y = 3x + 1  (**)

Substitute (*) to (**):

3x + 1 = x + 3      subtract 1 from both sides

3x = x + 2       subtract x from both sides

2x = 2        divide both sides by 2

Put the value of x to (*):

y = 1 + 3

the answer to the question is 7-3x.

Answer:

7 - 3x

Step-by-step explanation:

let "some number" = x

"3 times x" = 3(x)

"seven decreased by" 7 -

Put together the phrases.

"seven decreased by 3 times x" is 7 - 3x

7 - 3x is your answer

~

[tex]A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}[/tex]

Answer:

A'(3, - 1)

Step-by-step explanation:

Under a reflection in the y-axis

a point (x, y) → (- x, y), hence

A (- 3, - 1) → A'(3, - 1)

The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.

Given here: The coordinate of a Triangle A as (-3,-1)

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Thus The vertex of the triangle (-3,-1) it changes to (3,-1)

The algebraic representation for the transformation is given by '

(x,y)⇒(-1×x,1×y)

     ⇒(-x, y)

Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)

Learn more about cartesian coordinate system here:

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Answer:

40 cm

Step-by-step explanation:

Using the conversion

1 litre = 1000 cm³, then

40 litres = 40 × 1000 = 40000 cm³

The volume ( V) of a cuboid is

V = lbh ( divide both sides by bh )

l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm

Length of water tank is 40 cm

Given that;

Capacity of tank = 40 liters

Dimensions of tank = 50cm × 20cm

Find:

Length of water tank

Computation:

Capacity of tank = 40 liters

Capacity of tank = 40 × 1000

Capacity of tank = 40,000 cm³

Length of water tank = 40,000 / [50cm × 20cm]

Length of water tank = 40,000 / 1,000

Length of water tank = 40 cm

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Answer:

£ 75.60

Step-by-step explanation:

4 m ↔ £ 33.60

1 m ↔ £ 8.40

9 m ↔ £ 75.60

The cost of one meter of timber is £8.40, calculated by dividing £33.60 by 4. To find the cost of 9 meters, multiply £8.40 by 9, resulting in a total cost of £75.60.

To determine the cost of 9 meters of timber when we know that 4 meters cost £33.60, we can use a unit rate approach. First, we need to calculate the cost of one meter of timber by dividing the total cost by the number of meters. Then, we multiply the cost per meter by 9 to find the cost of 9 meters of timber.

Therefore, the cost of 9 meters of timber would be £75.60.

Answer:

A. 3 3/4

B. 4 5/9

C. 8 3/8

D. 12 3/11

E. 5 7/20

F. 2 145/174

Hope That Helps!

Answer,

(26/2) * 3

= 39

Explanation,

26 cookies is only 2/3 of 3/3. So, we divide 26 by 2 to see how many cookies are in 1/3. We then can find out that when you make 1/3 of the cookies there are 13. Since that is only 1/3 and we want to find out 3/3. We multiply 13 by 3 and get 39 which is all the cookies she planned to make.

Hope this helps :-)

Answer:

Since both sides equal, there are infinitely many solutions

Step-by-step explanation:

Simplify brackets

2/3×3/1=1

Use this rule: a/b×c/d=ac/bd

Simplify 2×3 to 6

6/3×2=1

Simplify 3×2 to 6

6/6=1

cancel 6

1=1

Since both sides equal, there are infinitely many solutions

Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.

Answer:

b.

Step-by-step explanation:

Interpret the meaning of the expression.

A.  

Julia's initial salary is $4,000, and the growth rate is 25% per year.

B.  

Julia's initial salary is $25,000, and the growth rate is 4% per year.

C.  

Julia's initial salary is $4,000, and the growth rate is 2.5% per year.

D.  

Julia's initial salary is $25,000, and the growth rate is 40% per year.

I can't exactly SHOW you where to put the numbers, but I can teach you the process of how you'd do it.

First off, label your number line from 0-15, as it is the simplest. (You'd be counting by 1 per each line). Then, follow this process:

1) Look at the first digit of your value. Place your number according to your first digit. (So, you'd put 0.365 at the 0 line and 3.521 at the 3 line)

2) Look at the second digit of your value. Imagine that between the two main lines (0-1 and 3-4) that there is 10 smaller lines. Then, you can place your number according to your second digit. (So, you'd put 0.365 at the 0.3 line and 3.521 at the 3.5 line).

3) Look at the third digit of your value. Imagine that between the two smaller lines (0.3-0.4 and 3.5-3.6) that there is 10 smaller lines. Then, you can place your number according to your third digit. (So, you'd put 0.365 at the 0.36 line and 3.521 at the 3.52 line).

4) Look at the fourth digit of your value. Imagine that between the two even smaller lines (0.36-0.37 and 3.52-3.53) that there is 10 smaller lines. Then, you can place your number according to your fourth digit. (So you'd place 0.365 at the 0.365 line and 3.521 at the 3.521 line)

the solutions to a general quadratic equation is

X=-b±√b²-4ac/2a  ,, When ax²+bx+c=0

the discriminant is the expression under the radical b²−4ac

Part A:

discriminant is (-16)² - 4(9)(60) = -1904

there are two complex solutions  

Part B:  

4x² + 8x − 5 = 0

4x² + 10x -2x - 5=0

2x ( 2x + 5) - 1(2 x + 5) =0  

(2x + 5)(2x-1) = 0

      /                     \

    /                          \

2x+5 = 0                 2x-1 =0    

x = -5/2                     x = 1/2

Answer:

The answer is $61.20

Step-by-step explanation:

First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.

Answer:

the answer might be 336 sorry if i am not right

Step-by-step explanation:

Answer:

I think the answer is approximately 5 packs of pencils.Hooe this helps :)

Step-by-step explanation: what I did was I multiplied 3 and 28 then divide that number by 12 and rounded my answer up.

Answer:

f(x)·g(x) = -6x² -x +77

Step-by-step explanation:

Given:

f(x) = 3x + 11

g(x) = -2x+7

f(x) * g(x) = (3x+11)*(-2x+7)

              = -6x²+21x-22x+77

              = -6x² -x +77

1. The answer is A.

Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.

2. The answer is A.

On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.

3. The answer is C.

If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.